NEW YORK – Before the participants in the 2013 All-Star Game took part in media sessions on Monday, they gathered in a hotel room to review the day’s schedule and what to expect from the horde of reporters chronicling the event.

As they seated themselves at a table before the meeting, several players said they looked around and realized that it was a Twins alumni reunion.

“They were everywhere,” Twins closer Glen Perkins said, “and there are a lot of guys that I played with.”

The number of former Twins at the All-Star Game reached eight Sunday when Grant Balfour was added to the American League roster to replace fellow Oakland righthander Bartolo Colon. The AL will be trying to snap a three-game losing streak in Tuesday’s 84th All-Star Game at City Field.

“It’s special,” former Twins closer Joe Nathan said of seeing so many former Minnesota teammates. “We got a chance to reminisce, talk about old times and talk about how guys are doing now. I’m sure in the clubhouse and maybe after the Home Run Derby we’ll get a chance to gather and chat some more.”

The eight All-Stars provide a great history lesson about Twins baseball in the 2000s.

Colorado’s Michael Cuddyer, Boston’s David Ortiz and Detroit’s Torii Hunter were on the 2002 team, the first Twins team to reach the postseason since 1991.

Nathan, Balfour and White Sox reliever Jesse Crain — who will miss Tuesday’s game because of an injury — joined the Twins in 2004 to help them sustain their dominance in the AL Central. Milwaukee’s Carlos Gomez (2009) and Baltimore’s J.J. Hardy (2010) represent the end of their dominance — six division titles in nine years — and their departures helped plant the seeds for the Twins’ plunge to the bottom of the division.

Perkins and catcher Joe Mauer will represent the Twins, raising the total to 10 players with current or past ties to the organization.

“It’s pretty cool,” Mauer said. “It’s kind of bittersweet. Obviously, you’d like to have all those guys in Twins uniforms here, but there’s great friendships with guys you played with. You carry on. You see your friends doing well. You always hope for that.”

That was the general reaction as the All-Star rosters were announced last week. Of course, there was also this reaction: Just think of where the Twins could be now.

No way of knowing

Hunter, who left the Twins as a free agent after 2007, falls into the latter category, seeing all the familiar faces Monday and pondering what might have been.

“It’s tough because that’s my home, that’s my love and no matter what that’s going to be my first love even if I play against them,” the nine-time Gold Glove outfielder said. “And it is tough to see them where they are at right now. With all these ex-Twin All-Stars here you’d think that if they would have kept us we would have been in the World Series.”

Twins first baseman Justin Morneau, who sent Cuddyer a congratulatory text message when the Rockies outfielder made the team, has a slightly different perspective.

“There’s nothing guaranteed that if they stayed here they would have become All-Stars more times,” said Morneau, an All-Star every year from 2007 to 2010. “I’m happy for all those guys. They deserve it. It would be nice to have them on our team, but [moving on] is part of the game.”

The Twins allowed Hunter, Cuddyer, Nathan, Balfour and Crain to leave via free agency, and Cuddyer and Nathan both left with concerns about the direction the team was headed. Ortiz, in a bad baseball decision, was released, signed by Boston and become Big Papi, one of the most feared hitters in the majors. Gomez was traded for Hardy. Hardy, in another bad baseball decision, was traded to Baltimore as the Twins decided to try Tsuyoshi Nishioka at shortstop.

Hardy doesn’t hold a grudge against the Twins because, he said, he didn’t give them a good reason to bring him back after he batted .268 with six homers and played in only 101 games in 2010. He has been healthy with the Orioles, providing smooth defense and some pop from the plate.

“I understand what’s going on there,” he said. “I didn’t play well. I played through the wrist injury. That’s all in the past and no hard feelings. After the 2010 season there were a lot of guys who departed Minnesota. They were looking to go in a different direction.”

The Twins, lacking the experience of several of the aforementioned players, lost a combined 195 games in 2011 and 2012, and are on pace to lose 94 games this season. Other than Gomez’s Brewers and Crain’s White Sox, the other ex-Twins All-Stars have realistic playoff hopes this season.

Impressed early

Nathan is surprised the Twins are where they are at. The Rangers split four games at Target Field in April and thought the Twins were very competitive.

“When we were there, we were actually impressed with how improved they were this year compared to last year,” Nathan said “They are going to do the right things to turn that thing around. They won’t sit back and let that thing go in the wrong direction.”

The Twins demoted three players to the minors Sunday in a roster shakeup and hope to be active before the July 31 trade deadline. But any turnaround will have to come from the core of current players — which includes a rotation that lacks front-end starters and youth at several key positions.

Hunter and Ortiz were on Twins teams that took their lumps from 1998 to 2001, then Cuddyer joined them in 2002 to form a club other franchises wanted to emulate in the 2000s.

They have moved on and thrived. And the things most of them learned as Twins have not been forgotten, the former Twins-turned-All-Stars say.

“It’s tough,” Cuddyer said. “I know those guys aren’t having fun. It’s hard to have fun when you are losing games, but you still have to go out and play and try to get things right. Try to get hot. Try to catch some kind his of spark in order to get that winning feeling back again.

“That’s mainly what it is. You have to get a mentality that you can go out there and win. That’s what we had those years in Minnesota. We felt like we couldn’t lose. Over the last few years, including my last year there, that mentality started to shift.’’